Alefacept is a drug tht may reduce the number of T cells in circulation. This drug has been used in the treatment of psoriasis, which is a skin disorder also caused by T cells, like chronic GVHD. Information from studies in psoriasis and in other patients with GVHD suggests that this drug may help to treat chronic GVHD. Chronic GVHD is a medical condition that can develop after allogeneic stem cell transplantation. It occurs when the donor immune cells (the "graft") attack and damage organs and tissue (the "host"). It is thought that T cells, a subtype of immune cells, are responsible for the tissue damage in chronic GVHD. In this research study we are looking to see how well Alefacept works in treating chronic GVHD that has not resolved after therapy with corticosteroids.